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Log-dimensional spectral properties of one-dimensional quasicrystals

Authors: David Damanik and Michael Landrigan
Journal: Proc. Amer. Math. Soc. 131 (2003), 2209-2216
MSC (2000): Primary 81Q10, 47B80
Published electronically: November 6, 2002
MathSciNet review: 1963769
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Abstract: We consider discrete one-dimensional Schrödinger operators on the whole line and establish a criterion for continuity of spectral measures with respect to log-Hausdorff measures. We apply this result to operators with Sturmian potentials and thereby prove logarithmic quantum dynamical lower bounds for all coupling constants and almost all rotation numbers, uniformly in the phase.

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Additional Information

David Damanik
Affiliation: Department of Mathematics 253–37, California Institute of Technology, Pasadena, California 91125

Michael Landrigan
Affiliation: Department of Mathematics, Idaho State University, Pocatello, Idaho 83209

Keywords: Schr\"odinger operators, Hausdorff dimensional spectral properties, Sturmian potentials
Received by editor(s): October 5, 2001
Received by editor(s) in revised form: February 23, 2002
Published electronically: November 6, 2002
Additional Notes: The first author was supported in part by the National Science Foundation through Grant DMS–0010101
The second author was supported in part by the National Science Foundation through Grant DMS-0070755
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2002 American Mathematical Society